Continuum robots offer a number of potential advantages over traditional rigid link robots in certain applications, particularly those involving reaching through complex trajectories in cluttered environments or where the robot must compliantly contact the environment along its length. The inherent flexibility of continuum robots makes them gentle to the environment, able to achieve whole arm manipulation, and gives rise to a unique form of dexterity—the shape of the robot is a product of both actuator and externally applied forces and moments. Thus, kinematic models which consider the effects of external loading have been active areas of recent research, and models that consider pneumatic actuation, multiple flexible push-pull rods, and a elastic member consisting of concentric, pre-curved tubes, have recently been derived.
Cosserat rod theory has shown promise as a general tool for describing continuum robots under load, but application of the theory to tendon-actuated continuum robots has not yet been fully explored. Simplified beam mechanics models have been widely used to successfully obtain free-space kinematic models for tendon-actuated robots. The consensus result is that when the tendons are tensioned, the elastic member assumes a piecewise constant curvature shape. This approach is analytically simple and has been thoroughly experimentally vetted on several different robots. However, this approach is limited in that it cannot be used to predict the large spatial deformation of the robot when subjected to additional external loads. Cosserat rod theory provides the modeling framework necessary to solve this problem, and initial work towards applying it to tendon actuated robots has been performed by considering planar deformations and using the simplifying assumption that the load from each tendon consists of a single point moment applied to the rod at the termination arc length. However, such models are limited.